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On a local to global principle in étale K-groups of curves

Published online by Cambridge University Press:  17 May 2013

Grzegorz Banaszak  and
Piotr Krasoń
Grzegorz Banaszak
Affiliation:
Department of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Polandbanaszak@amu.edu.pl
Piotr Krasoń
Affiliation:
Department of Mathematics and Physics, Szczecin University, 70-415 Szczecin, Polandkrason@wmf.univ.szczecin.pl
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Abstract

Let X be a smooth, proper and geometrically irreducible curve X defined over a number field F and let χ be a regular and proper model of X over OF,Sl. In this paper we address the problem of detecting the linear dependence over ℤl of elements in the étale K-theory of χ. To be more specific, let P ∊ Ket2n(χ) and let ⋀̂ ⊂ Ket2n(χ) be a ℤl-submodule. Let rυ: Ket2n(χ) → Ket2n(χυ) be the reduction map for υ ∉ Sl.We prove, under some conditions on X, that if rυ() ∈ rυ (⋀̂) for almost all υ of then ∈ ⋀̂ + Ket2n(χ)tor.

Keywords

étale K-theoryalgebraic curveJacobian varietythe reduction mapPrimary 19FxxSecondary 11Gxx

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Type
Research Article
Information
Journal of K-Theory , Volume 12 , Issue 1: Nanjing Special Issue on K-theory, number theory and geometry , August 2013 , pp. 183 - 201
Copyright
Copyright © ISOPP 2013 

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